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Access this online resource for additional instruction and practice with linear function models.

Key concepts

  • We can use the same problem strategies that we would use for any type of function.
  • When modeling and solving a problem, identify the variables and look for key values, including the slope and y -intercept. See [link] .
  • Draw a diagram, where appropriate. See [link] and [link] .
  • Check for reasonableness of the answer.
  • Linear models may be built by identifying or calculating the slope and using the y -intercept.
    • The x -intercept may be found by setting y = 0 , which is setting the expression m x + b equal to 0.
    • The point of intersection of a system of linear equations is the point where the x - and y -values are the same. See [link] .
    • A graph of the system may be used to identify the points where one line falls below (or above) the other line.

Section exercises

Verbal

Explain how to find the input variable in a word problem that uses a linear function.

Determine the independent variable. This is the variable upon which the output depends.

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Explain how to find the output variable in a word problem that uses a linear function.

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Explain how to interpret the initial value in a word problem that uses a linear function.

To determine the initial value, find the output when the input is equal to zero.

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Explain how to determine the slope in a word problem that uses a linear function.

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Algebraic

Find the area of a parallelogram bounded by the y -axis, the line x = 3 , the line f ( x ) = 1 + 2 x , and the line parallel to f ( x ) passing through ( 2 , 7 ) .

6 square units

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Find the area of a triangle bounded by the x -axis, the line f ( x ) = 12 1 3 x , and the line perpendicular to f ( x ) that passes through the origin.

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Find the area of a triangle bounded by the y -axis, the line f ( x ) = 9 6 7 x , and the line perpendicular to f ( x ) that passes through the origin.

20.01 square units

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Find the area of a parallelogram bounded by the x -axis, the line g ( x ) = 2 , the line f ( x ) = 3 x , and the line parallel to f ( x ) passing through ( 6 , 1 ) .

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For the following exercises, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped 4,700. Assume this trend continues.

Predict the population in 2016.

2,300

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Identify the year in which the population will reach 0.

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For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues.

Predict the population in 2016.

64,170

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Identify the year in which the population will reach 75,000.

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For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.

Find the linear function that models the town’s population P as a function of the year, t , where t is the number of years since the model began.

P ( t ) = 75 , 000 + 2500 t

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Find a reasonable domain and range for the function P .

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If the function P is graphed, find and interpret the x - and y -intercepts.

(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.

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Questions & Answers

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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